Jeff Gruszynski, wrote an answer in [1] related the question, "Why are direct band gap materials preferred over indirect band gap materials for optical properties?". below I cite the following:
A direct gap semiconductor DOES NOT require a phonon in a photon-to- electron-hole pair generation process so electrooptical devices is very efficient.
An indirect gap semiconductor DOES require a phonon in a photon-to-electro-hole pair generation process.
In the case of light generation, the indirect gap material creates a phonon which is instead emitted and creates heat that must be dissipated. A direct gap semiconductor can generate photons with less heat produced because it doesn’t generate a phonon with each electron-hole photo-recombination.
I hope the above comparison is sufficient for you to decide which one is more important for your application . My best regards ...